关于多元线性混合模型中方差分量矩阵的估计.pdfVIP

T itle: Estimation of Variance Components M atrix in Multivariate Linear Mixed Model M ajor:Probability and Mathematical Statistics Name: Xiaoling Kong Signature Supervisor:Professor Jianhong Shi Signature A bstract The aim of this thesis is to study the estimation of variance components matrices in general multivariate linear mixed model with two variance components matrices. The first chapter introduces the general multivariate linear mixed model with two variance components matrices, theories and methods which including least square method, the spectral decomposition estimation method and Wishart distribution definitions and properties. For the general multivariate linear mixed model with two variance components matrices, based on the spectral decomposition of the covariance matrix, the second chapter gives a new spectral decomposition estimation of variance components matrices. In the third chapter, the new spectral decomposition estimation and the analysis of variance estimation are compared, a relationship between the two estimates is established, and some conditions are found under which one estimate is superior to the other in terms of the squared error loss function. Through studying a class of estimators, in the sense of squared error risk, a better estimation is derived, which has smaller non-negative probability. In the fourth chapter, in view of the new spectral decomposition and analysis estimation of variance components matrices, we obtained the estimation of covariance matrix. In the sense of squared error risk, we discussed the superiority of SDE and ANOVAE when the model is balanced and unbalanced. 【Key Words 】 multivariate mixed linear models variance components matrix spectral decomposition e